Question

You win a game with probability 0.511. Each game you play is independent. If you play the game 10 times, What is the probability that you win 6 of the 10 times.

Answer #1

**This is clearly a BINOMIAL EXPERIMENT, because of the
following reasons.**

**1) Number of games played i.e number of trials =10 is
fixed.**

**2)All the games are independent and identical in the
aspect of winning.**

**3) Considering a game it results in two outcomes either
win(success) or lose(failure).**

**4) Probability of winning i.e probability of success =
0.511 is same for every game.**

**Now let X be the number of games win out of 10
games.**

**Then we need to find P(X=6).**

**Formula:**

**P(X=x) = ncx .
p^x . q^n-x .**

**Here n= 10, X= 6, p = 0.511, q=1-p=0.489**

**So, P(X=6) = 10c6 . (****0.511)^6 .
(0.489)^10-6 .**

**= 0.2138
answer.**

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